1. 题目1

8个球找出那个偏重的球，其他7个球重量一样，有天平称重左右两边

//
// Created by ZhuanZ1 on 2026/6/23.
//


#include <iostream>
#include <vector>
using namespace std;
#include <optional>

// 模拟天平的三种状态（三进制信息源）
enum class ScaleState {
    LEFT_HEAVY,   // 左重
    BALANCED,     // 平衡（核心排除状态）
    RIGHT_HEAVY   // 右重
};

// 模拟天平称重函数
// left_indices: 左盘球的索引集合
// right_indices: 右盘球的索引集合
// weights: 所有球的实际重量数组
ScaleState weigh(const vector<int>& left_indices,
                 const vector<int>& right_indices,
                 const vector<int>& weights)
{
    int left_sum = 0, right_sum = 0;
    for (int idx : left_indices)  left_sum += weights[idx];
    for (int idx : right_indices) right_sum += weights[idx];

    if (left_sum == right_sum) return ScaleState::BALANCED;
    return (left_sum > right_sum) ? ScaleState::LEFT_HEAVY : ScaleState::RIGHT_HEAVY;
}

// 核心求解函数：返回异常球的索引
int findAbnormalBall(const vector<int>& weights) {
    // 【第1次称重】左3 vs 右3
    vector<int> left  = {0, 1, 2};
    vector<int> right = {3, 4, 5};
    ScaleState state1 = weigh(left, right, weights);

    if (state1 == ScaleState::BALANCED) {
        // 异常球在 {6, 7} 中，已知偏重
        ScaleState state2 = weigh({6}, {0}, weights); // 0是已知正常球
        return (state2 == ScaleState::BALANCED) ? 7 : 6;
    }

    // 已知偏重，所以哪边重，异常球就在哪边
    vector<int> suspect3 = (state1 == ScaleState::LEFT_HEAVY) ? vector<int>{0, 1, 2} : vector<int>{3, 4, 5};

    // 【第2次称重】从3个嫌疑球中取2个对比
    ScaleState state2 = weigh({suspect3[0]}, {suspect3[1]}, weights);

    if (state2 == ScaleState::BALANCED)   return suspect3[2]; // 没上秤的那个
    if (state2 == ScaleState::LEFT_HEAVY) return suspect3[0]; // 左重→左边是重球
    return suspect3[1];                                        // 右重→右边是重球
}

int main() {
    // 测试用例：8个球，正常重量为10，异常球(索引7)重量为12
    vector<int> balls = {10, 10, 10, 10, 10, 10, 10, 12};

    vector<int> balls2 = {10, 12, 10, 10, 10, 10, 10, 10};

    int result = findAbnormalBall(balls2);

    if (result != -1) {
        std::cout << "找到异常球！索引: " << result
                  << ", 重量: " << balls[result] << std::endl;
    }
    return 0;
}